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2017 East Central NA Regional Contest

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2017-10-28 19:00 UTC

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Problem GA Question of Ingestion

Stan Ford is a typical college graduate student, meaning
that one of the most important things on his mind is where his
next meal will be. Fortune has smiled on him as he’s been
invited to a multi-course barbecue put on by some of the
corporate sponsors of his research team, where each course
lasts exactly one hour. Stan is a bit of an analytical type and
has determined that his eating pattern over a set of
consecutive hours is always very consistent. In the first hour,
he can eat up to $m$
calories (where $m$
depends on factors such as stress, bio-rhythms, position of the
planets, etc.), but that amount goes down by a factor of
two-thirds each consecutive hour afterwards (always truncating
in cases of fractions of a calorie). However, if he stops
eating for one hour, the next hour he can eat at the same rate
as he did before he stopped. So, for example, if $m=900$ and he ate for five
consecutive hours, the most he could eat each of those hours
would be $900$,
$600$, $400$, $266$ and $177$ calories, respectively. If,
however, he didn’t eat in the third hour, he could then eat
$900$, $600$, $0$, $600$ and $400$ calories in each of those hours.
Furthermore, if Stan can refrain from eating for two hours,
then the hour after that he’s capable of eating $m$ calories again. In the example
above, if Stan didn’t eat during the third and fourth hours,
then he could consume $900$, $600$, $0$, $0$ and $900$ calories.

Stan is waiting to hear what will be served each hour of the
barbecue as he realizes that the menu will determine when and
how often he should refrain from eating. For example, if the
barbecue lasts $5$ hours
and the courses served each hour have calories $800$, $700$, $400$, $300$, $200$ then the best strategy when
$m=900$ is to eat every
hour for a total consumption of $800+600+400+266+177 = 2\, 243$
calories. If however, the third course is reduced from
$400$ calories to
$40$ calories (some
low-calorie celery dish), then the best strategy is to not eat
during the third hour — this results in a total consumption of
$1\, 900$ calories.

The prospect of all this upcoming food has got Stan so
frazzled he can’t think straight. Given the number of courses
and the number of calories for each course, can you determine
the maximum amount of calories Stan can eat?

Input

Input starts with a line containing two positive integers
$n$$m$ ($n
\leq 100, m \leq 20\, 000$) indicating the number of
courses and the number of calories Stan can eat in the first
hour, respectively. The next line contains $n$ positive integers indicating the
number of calories for each course.